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Full text of "Analytical Mechanics"

CHAPTER XIII. ANGULAR IMPULSE AND  ANGULAR MOMENTUM.
206. Angular Impulse.  The mechanical results produced by a torque may be measured in two ways. If the torque is considered to act through an angle the result measured is the work done by the torque; on the other hand if the torque is considered to act during an interval of time the result measured is called angular impulse.
The angular impulse which a constant torque imparts to a. body in an interval of time equals the product of the torque by the interval of time. If H denotes the angular impulse^, G the torque, and t the time of action, then
H = G  t.                                  (10
When a vector is multiplied by a scalar the product is a vector which has the same direction as the original vector. Therefore H is a vector .and has the same direction as G.
When torque is not constant angular impulse equals the vector sum of infinitesimal impulses imparted during infinitesimal intervals of time. Therefore
H-/'.
Jo
Gdt
= PM
Jo
/*CO
= /   Jd<o,
(I)
where co0 and o are the angular velocities at the beginning, and at the end of the interval of time during which the torque acts.
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